The role of chalcogen vacancies for atomic defect emission in MoS2

For two-dimensional (2D) layered semiconductors, control over atomic defects and understanding of their electronic and optical functionality represent major challenges towards developing a mature semiconductor technology using such materials. Here, we correlate generation, optical spectroscopy, atomic resolution imaging, and ab initio theory of chalcogen vacancies in monolayer MoS2. Chalcogen vacancies are selectively generated by in-vacuo annealing, but also focused ion beam exposure. The defect generation rate, atomic imaging and the optical signatures support this claim. We discriminate the narrow linewidth photoluminescence signatures of vacancies, resulting predominantly from localized defect orbitals, from broad luminescence features in the same spectral range, resulting from adsorbates. Vacancies can be patterned with a precision below 10 nm by ion beams, show single photon emission, and open the possibility for advanced defect engineering of 2D semiconductors at the ultimate scale.


Introduction
Control over atomic defects is the foundation of today's semiconductor technology. For two-dimensional van der Waals semiconductors, the term "defect engineering" has been coined to suggest that, by introducing defects, these materials can be engineered beyond the established concepts of doping or alloying 1 , enabling advanced functionality, such as single photon sources 2,3 or photocatalysis with chemical speci city 1 . Nevertheless, the microscopic understanding of defect-related modi cations remains elusive due to a lack of thorough correlation between atomic structure and resulting macroscopic electronic and optical properties. Combing controlled defect engineering with optical spectroscopy as well as atomic imaging and ab-initio theory, we identify the optical signature of pristine chalcogen vacancies in MoS 2 . Vacancies introduce a deep center with sharp optical emission, markedly different from previously observed broad luminescence bands. [4][5][6][7][8] Comparing annealed vs. He-ion treated MoS 2 , we establish that the recently discovered single-photon emitters in He-ion irradiated MoS 2 originate from chalcogen vacancies 3 . The latter can be deterministically created with a precision below 10 nm 9 , underscoring the potential of defect engineering for two-dimensional (quantum-) optoelectronics.
In semiconductors, the interaction of free excitons with the Coulomb potential of lattice defects results in localized defect-exciton complexes 10 . In the traditional picture, exciton localization at shallow defects introduces an additional binding energy. Therefore, optical signatures of defects lie energetically below the free exciton 10 . Defect levels deep inside the band gap provide further relaxation pathways at even lower transition energies 10 . Since in two-dimensional (2D) semiconducting transition metal dichalcogenides, including MoS 2 , MoSe 2 , WS 2 and WSe 2 , the screening of the defect potential is weak, and also the exciton Bohr radius is small (~ 2 -3 nm) 11 , excitons are extremely con ned in real space when coupling to defects 12 . Therefore, as shown theoretically for MoSe 2 and MoS 2 , chalcogen vacancy Page 4/12 levels give rise to a series of strongly bound defect excitons which then hybridize with excitonic states of the pristine system 12,13 .
At low-temperatures, most 2D semiconductors exhibit broad sub-gap emission extending several hundred meV below the exciton 4,5,7,8,14 . Generally, this sub-gap luminescence becomes stronger with increasing number of point defects present in the TMD layer, and it is often called L-band (emphasizing localization) or D-band (emphasizing defects) in the literature. The correlation between defects and the L-band was found either by introducing additional defects 5,14 or by correlating spatial uctuations of the existing defect density and excitonic properties 4,15 . Nevertheless, there is a surprising lack of consensus about the origin for such broad defect emission. Some studies emphasized radiative recombination at intrinsic point defects as underlying mechanism 4,7 . Other studies highlighted the relevance of molecular adsorbates. For example, calculations show that adsorbed molecular oxygen modi es the electronic structure of the sulfur vacancy in MoS 2 , either by removing the in-gap state 16 or by p-doping via hole transfer from oxygen 6 . Furthermore, it has been suggested that laser illumination incorporates atomic oxygen into pre-existing chalcogen vacancies either by photo-assisted dissociation of molecular oxygen 17 or water 18 . However, chalcogen vacancies are likely already passivated by atomic oxygen in asprepared TMDs 9,19,20 . Moreover, several studies demonstrated that laser annealing in controlled gas environments 21,22 or encapsulation in hBN 23 can completely remove the L-band suggesting chemisorbed or physisorbed molecules as its origin 22 .
By contrast, a spectrally sharp sub-gap luminescence and single photon emission was also reported at low-temperatures 2 . As the microscopic model, a combination of strain potentials, which funnel and localize excitons, and atomic defects, which provide recombination centers for localized excitons, was suggested 2 . While these point-like emitters appear randomly in as-prepared samples, they can be generated deterministically via engineered nanoscale strain potentials 2 . Recently, our group has demonstrated that atomic point defects, which are created deterministically by He-ion irradiation 9 , act as narrow and reproducible single-photon emitters, yet without a local strain potential 3,24 . Here, we disentangle broad defect emission due to adsorbates, which can be desorbed by in-vacuo annealing at moderate temperatures, and narrow defect emission via sulfur vacancies, which are generated both by annealing at high temperatures and He-ion irradiation. Figure 1 shows low-temperature photoluminescence (PL) spectra of monolayer MoS 2 on hexagonal boron nitride (hBN). In addition to exciton ( 0 X A ) and trion ( -X A ), 11 as-exfoliated MoS 2 exhibits a prominent L-band from approximately 1.5 eV to 1.9 eV (Fig. 1a). Mild annealing (T annealing = 500 K) in vacuum results in a striking reduction of the L-band (Fig. 1b), presumably due to desorption of adsorbates. Further annealing at high temperature (T annealing = 800 K) introduces a narrow peak X L at 1.75 eV (Fig. 1c). A similar, yet even sharper, spectral signature is observed in fully encapsulated MoS 2 after He-ion irradiation ( Fig. 1d). The improved inhomogeneous broadening agrees with previous studies of fully hBN encapsulated heterostructures 23 . In the following, we show that adsorbates introduce a continuum of defect states, which is responsible for the L-band emission, whereas pristine sulfur vacancies introduce a deep center, which is very likely also the origin of recently discovered single photon emission in He-ion treated MoS 2 . 3,24 Figure 2 shows low-temperature PL of MoS 2 after stepwise in-vacuo annealing up to 800 K. In each cycle, the samples were rapidly annealed in a customized cryostat for 30 min and then cooled back to cryogenic temperature (T sample ~ 20 K) for PL characterization maintaining a high vacuum (p < 10 -4 mbar) at all times (Supplementary Information S1). Figure 2a illustrates spectra of as-exfoliated MoS 2 on hBN and after several mild annealing steps to 420 K, 450 K, and 510 K. Again, the as-exfoliated ake exhibits a prominent L-band (cf. Fig. 1a). The intensity of the L-band decreases relative to the intensity of the free exciton emission by one order of magnitude after annealing to T annealing = 420 K, and it gradually disappears for higher annealing temperatures (Fig. 2b) . Furthermore, the trion emission decreases initially compared to the free exciton indicating a reduced doping, as observed previously in TMDs during desorption of physisorbed gas 25 and chemical dopants 26 . Hence, we attribute the L-band to adsorbates, which are progressively removed during the mild annealing steps. The desorption does not follow a simple Arrhenius law, since it depends on the total number of adsorbates, which is unknown. Therefore, we can estimate only an upper bound of ~100 meV for the desorption barrier, which agrees with ab-initio studies for molecular adsorbates on MoS 2 27 and temperature programmed desorption on bulk MoS 2 28 .

Results
At T annealing = 510 K, a spectrally narrow emission line X L appears around 1.75 eV. In contrast to the Lband, the intensity of X L increases with higher annealing temperatures, until the whole PL signal disappears at T annealing > 700 K (see Supplementary Information S2). To extract the thermal activation barrier of X L , we use an hBN/MoS 2 /hBN heterostack, where the L-band is already suppressed in the asprepared structures. As seen in Fig. 2c, X L brightens in the encapsulated monolayer with increasing annealing temperature, and further narrows after annealing to 800 K indicating a complete removal of residual adsorbates. At even higher temperatures (T annealing = 900 K), the intensity of X L decreases drastically, followed by the complete disappearance of the overall PL (Supplementary Information S2).
Consistent with saturating a nite density of localized defect levels, X L exhibits a saturating behavior as function of excitation power (see Supplementary Information S3) 24 . In a simple rate equation model, the saturated defect emission is then proportional to the total number of emission centers. In this case, we can readily determine the energy barriers for defect generation since it is proportional to the difference in the integrated spectral weight of X L compared to the previous annealing step. For example, the number of defects generated during annealing at 600 K is proportional to the difference in integrated PL intensity, which we label ΔInt(X L ), after annealing to 600 K and 510 K. In the limit of low density, defect generation is independent of the number of existing defects, and we expect a simple Arrhenius law. From Fig. 2d, we nd an activation energy of (0.71 ± 0.13) eV for the X L -peak consistent with theoretical predictions for the formation energy of mono-sulfur vacancies (approximately 1 eV) 29,30 . Interstitial sulfur defects should not form under high-vacuum, i.e. sulfur-poor, conditions 29 . The formation energies for transition metal vacancies are much larger (3 eV -8 eV) 29,30 . Consequently, the formation of sulfur vacancies during annealing is thermodynamically the most favorable and, therefore, most likely process.
We continue to corroborate the dominant generation of sulfur vacancies during annealing by atomicscale characterization. Here, we perform high-resolution low-temperature scanning tunneling microscopy (STM) and atomic force microscopy (AFM) of single-layer MoS 2 before and after high-temperature annealing in vacuum (T annealing > 500 K) as well as before and after He-ion irradiation. These experiments are conducted on graphene/SiC heterostructures. The graphene substrate is essential as conductive support, but it quenches. the optical emission from defects ( Supplementary Information S7) 31 . For STM, all samples were prepared in-vacuo by a mild annealing step in vacuum (T annealing < 500 K) to remove adsorbates. In agreement with our optical studies, the surface of MoS 2 is virtually free from adsorbates after mild annealing. By far the most dominant defects in pristine material were oxygen atoms substituting sulfur, but no sulfur vacancies were observed (Supplementary Information S5) 9,19,20 .
After additional high-temperature annealing, we observed only two additional types of defects within our experimental statistics (Fig. 3). Their high-resolution STM topography exhibits a trigonal symmetry (Figure 3a and 3b shaped, whereas the bottom vacancy appears triangular-shaped with bright maxima at the corners. These same defects, i.e. top and bottom sulfur vacancies, were also con rmed in the He-ion irradiated samples ( Fig. 3e and Fig. 3f). For He-ion treated samples, sulfur vacancies are the dominant defect type, among other defects that are generated with lower yield 9 . Furthermore, we performed CO-tip AFM on the sulfur vacancies (Figure 3g and Fig. 3h). For the top vacancy, we observe an apparent depression at the sulfur site, whereas for the bottom vacancy structural relaxation results in a slight protrusion, in agreement with previous studies on WS 2 20 . Most importantly, AFM conclusively assigns the defect onto the sulfur sublattice, which is di cult from STM alone 20 . Overall, the scanning probe experiments con rm the composition and surface condition of MoS 2 derived from optical characterization (cf. Fig. 1). From our different annealing experiments, we conclude that defect luminescence X L at 1.75 eV arises from pristine, i.e. undecorated, sulfur vacancies. We note that, there are at least two pathways for formation of sulfur vacancies, which are desorption of a sulfur atom or desorption of an oxygen atom from a sulfur site. The latter substitute for sulfur in as-prepared TMDs 19,20 . Based on the similarity of the optical spectra and the abundance of sulfur vacancies in thermally annealed as well as in He-ion irradiated MoS 2 (cf. Figure 1), we propose that also the origin of quantum emission from individual He-ion induced defects is due to the (non-passivated) sulfur vacancy 24 . For the experimental curves, vacancies were introduced in fully encapsulated MoS 2 both by in-vacuo thermal annealing and by ex-situ helium ion modi cation. All spectra are referenced to the neutral exciton transition, where we found 1.89 eV for the calculated spectrum and 1.96 eV (1.94 eV) for the measured annealed (ion-modi ed) spectrum. Notably, while the dominant defect emission (X L ) occurs about 0.2 eV below 0 X A , we consistently observe weak emission features (red arrows) at even lower energies 3 . The multiple sub-gap emission peaks are qualitatively in agreement with the ab-initio calculations of excitonic defect states (top panel of Fig. 4b). Although absorbance cannot strictly be used to infer emission properties, we identify possible transitions based on the correspondence between calculated absorbance and experimental emission spectrum. Within the computational uncertainty, the defect emission at 1.75 eV agrees with the energy range where calculations predict dominant contributions from defect to defect transitions (D 2 ). Figure 4c further corroborates this assignment. Here, we plot the emission spectrum of a single defect, which was generated by He-ion bombardment 9,24 , for co-and cross-circularly polarized excitation and detection. We do not detect a valley polarization, as expected for a transition that occurs between localized defect levels. Therefore, we conclude that the X L peak observed in our thermally annealed as well as He-ion treated MoS 2 monolayers arises due to a localized excitonic transition between the defect orbitals of the pristine sulfur vacancy.
Typically, the dominant emission process should involve the lowest energy state of the system, i.e. transitions of type D 1 . However, in our experiments, the defect emission is governed by transitions of intermediate energy, i.e. transitions of type D 2 , although the calculated oscillator strength varies only weakly in the relevant regime. A naïve scenario to explain our observations involves a relaxation cascade after the absorption process: optical excitation creates a free exciton, which gets localized, and then both hole and electron decay into a defect state (type D 2 ). If further relaxation of the captured exciton into an excitonic state of type D 1 is slow or prohibited, the emission will occur dominantly from the fully localized electron and hole state. From a theory point of view, the above picture demands to include further interactions, such as exciton-exciton or exciton-phonon coupling 34 .
In summary, by combining far-eld optical spectroscopy, atomic-resolution scanning probe microscopy, and ab-initio theory, our study provides compelling evidence of optical defect emission from pristine sulfur vacancies in single layer MoS 2 . In contrast to previous studies, these pristine sulfur vacancies are generated in-vacuo or capped by hBN, and therefore, neither passivated by oxygen nor decorated with adsorbates. Similar to previous reports, we observe a broad L-band luminescence due to adsorbates in as-prepared MoS 2 monolayers, which can be suppressed by a combination of h-BN encapsulation and mild annealing. In as-prepared layers and after mild annealing, pristine sulfur vacancies are absent, and oxygen passivated vacancies are the dominant defect. We suggest that oxygen-passivated vacancies form active sites for adsorption of molecular species, since many previous studies established a positive correlation between sulfur de ciency and defect emission 4,5,15 . Pristine vacancies are created in h-BN/MoS 2 /h-BN heterostructures either via in-vacuo thermal annealing or ex-situ helium ion bombardment, whereby the latter allows generating single photon emitters on demand 24 with a position accuracy below 10 nm 9 . Guided by ab-initio calculations, we identify transitions between a localized ingap defect state and a localized resonant defect state as the most likely candidate.

Methods
Sample preparation. We micromechanically exfoliated MoS 2 (SPI Supplies) and hBN (NIMS, K.W. and T.T.) using adhesive tape. We used an all-dry viscoelastic stamping technique to transfer single akes to a substrate consisting of SiO 2 /Si or epitaxial graphene on (6H)-SiC using a polydimethylsiloxane (PDMS) stamp. During the transfer, we heated the samples to approximately 60°C, to increase the transfer probability. We cleaned the samples with acetone, isopropanol, and nitrogen gas after each stacking step to remove residues and increase the adhesion.
In-vacuo annealing. We annealed all samples in a modi ed optical cryostat (Janis ST-500). A customized heater was added to the cryostat for rapid thermal cycling between cryogenic temperatures (T sample ~ 20 K) and high temperatures (T sample ~ 900 K). We determined the annealing temperature at the sample with a thermocouple. We rapidly ramped to the desired annealing temperature and kept it constant for 30 minutes, then we cooled the sample with the highest possible rate back to cryogenic temperatures and conducted the PL measurements.
Photoluminescence spectroscopy. The annealed samples were studied with a custom microscope set-up (λ excitation = 532 nm, Nikon Plan Fluor ELWD 20x/0.45, WD 7.4 mm). The cryostat was mounted on a motorized xy-stage (ASI) with a minimum stepsize of 100 nm. The emitted light was focused onto the entrance slit of the spectrometer (Andor Kymera 328, grating 300 grooves/mm) and the signal was collected by a CCD camera (Andor iXon). The valley polarization measurements of the ion-treated samples were carried out in He-ow cryostat at T = 10 K (λ excitation = 590 nm, Mitutoyo 100x/0.5 M Plan Apo NIR, WD 12 mm, PI Acton SP-2500i spectrometer, grating 300 grooves/mm). The circular polarization was adjusted using an achromatic λ/4-plate in front of the objective lens. The emitted light passed again through the same waveplate, and the polarization was analyzed using a linear polarizer.
Scanning probe microscopy. We performed combined scanning tunneling microscopy and atomic force microscopy (Createc) at low temperatures (T ~ 6 K) in vacuum with a base pressure of around 10 -10 mbar. All samples were treated by mild annealing (T ~ 500 K) under UHV conditions for 10 -20 minutes. All STM images were recorded using the constant-current feedback and current setpoint of I t = 100 pA.
Chemically etched tungsten tips were sharpened by repeated indentations into a Au(111) substrate. All AFM images were recorded with a qPlus quartz crystal tuning fork in constant height mode with an applied bias voltage V bias = 0 V.
Helium ion microscopy. Single layer MoS 2 akes supported by graphene/SiC were nanostructured using a helium ion microscope (HIM ORION NanoFab, Zeiss). The whole MoS 2 ake was exposed to a constant helium ion dose of 5·10 14 cm -2 . We operated the HIM at a helium pressure of 2.5·10 -6 Torr, a beam energy of 30 keV, beam current of 0.7 pA, pixel spacing of 5 nm, and eld of view (FOV) of 100 µm. To obtain the desired constant helium ion dose, the dwell time was adapted to the beam current.
Theoretical calculations. DFT calculations of the defect orbitals in Fig. 3 were performed using the Vienna Ab initio Simulation Package, VASP 5.4.4 35 . Details can be found in Supplementary information S7. The GW-BSE approach used to calculate the absorbance spectra of MoS 2 with sulfur vacancies in References